Studying cells: modern microscopy and quantitative cell biology

Cell biology is the study of how cells are organized and how their parts work together. Earlier courses introduced the basic tour: BIOL-107 described the organelles of a typical eukaryotic cell, the light and electron microscopes, cell fractionation and the limits set by the wavelength of light. This course goes inside each compartment in depth, asking how a cell builds and maintains its internal organization, how proteins find their way to the right place, how the cytoskeleton shapes and moves the cell, how cells stick together and talk to each other, and how they decide when to divide or die. Throughout, the emphasis is quantitative: how big, how many, how fast. This first lesson is about the tools that make such questions answerable. Modern cell biology rests on fluorescent probes that label specific molecules in living cells, on microscopes that beat the classical limit of resolution, on cryo-electron methods that show molecular machines in their natural setting, and on image analysis that turns pictures into numbers.

Why measurement matters

For most of the twentieth century, cell biology was largely descriptive. Electron micrographs of the 1950s and 1960s, many made by George Palade, Keith Porter and their colleagues, revealed the endoplasmic reticulum, the Golgi apparatus, mitochondrial cristae and the double nuclear envelope. These images defined the compartments that this course is about. But a picture of a fixed cell is a single frame from a film, and it does not say how fast molecules move, how many copies of a protein are present or how long a structure lasts. Today the questions are dynamic and quantitative. How quickly does a membrane protein diffuse? What fraction of a receptor sits on the cell surface rather than inside? How many microtubules grow from a centrosome each minute? Answering them requires both the right probes and careful measurement.

A useful starting point is to know how large a typical cell is and how its volume and membranes are divided among compartments. Morphometric studies, which estimate volumes and areas from many thin sections using the principles of stereology, have given such numbers for well-studied cells such as rat liver hepatocytes and pancreatic acinar cells.

Two lessons stand out from such data. First, internal membranes vastly outnumber the plasma membrane: in a hepatocyte, the plasma membrane is only about 2 per cent of the total membrane area, and the endoplasmic reticulum alone accounts for half. Second, membranes and organelles occupy nearly half of the cell, so the cytoplasm is not a bag of fluid but a densely packed, structured space.

# Stereology: converting volume and membrane fractions into absolute amounts
# Illustrative hepatocyte: volume about 5,000 um^3,
# total membrane area about 110,000 um^2 (approximate textbook values)
cell_volume = 5000.0      # um^3
total_membrane = 110000.0 # um^2

volume_fraction = {"cytosol": 0.54, "mitochondria": 0.22, "rough ER": 0.09,
                   "smooth ER + Golgi": 0.06, "nucleus": 0.06, "peroxisomes": 0.01,
                   "lysosomes": 0.01, "endosomes": 0.01}
membrane_fraction = {"plasma membrane": 0.02, "rough ER": 0.35, "smooth ER": 0.16,
                     "Golgi": 0.07, "mitochondrial outer": 0.07, "mitochondrial inner": 0.32}

for name, f in volume_fraction.items():
    print(f"{name:22s} {f*100:4.0f}%  ~{f*cell_volume:7.0f} um^3")
print()
for name, f in membrane_fraction.items():
    print(f"{name:22s} {f*100:4.0f}%  ~{f*total_membrane:8.0f} um^2")

# How many times larger is the ER membrane than the plasma membrane?
er = membrane_fraction["rough ER"] + membrane_fraction["smooth ER"]
print(f"\nER membrane / plasma membrane = {er / membrane_fraction['plasma membrane']:.0f}x")

cytosol                  54%  ~   2700 um^3
mitochondria             22%  ~   1100 um^3
rough ER                  9%  ~    450 um^3
smooth ER + Golgi         6%  ~    300 um^3
nucleus                   6%  ~    300 um^3
peroxisomes               1%  ~     50 um^3
lysosomes                 1%  ~     50 um^3
endosomes                 1%  ~     50 um^3

plasma membrane           2%  ~    2200 um^2
rough ER                 35%  ~   38500 um^2
smooth ER                16%  ~   17600 um^2
Golgi                     7%  ~    7700 um^2
mitochondrial outer       7%  ~    7700 um^2
mitochondrial inner      32%  ~   35200 um^2

ER membrane / plasma membrane = 26x

Fluorescent proteins changed everything

The single most important tool of modern cell biology is the ability to make a specific protein glow inside a living cell. In 1962 Osamu Shimomura purified green fluorescent protein (GFP) from the jellyfish Aequorea victoria. In 1994 Martin Chalfie showed that the cloned GFP gene could be expressed in other organisms, producing fluorescence without any added cofactor, and Roger Tsien engineered variants with brighter fluorescence and new colours. The three shared the 2008 Nobel Prize in Chemistry. Today a researcher can fuse the coding sequence of a fluorescent protein to the gene of interest, often at the gene’s natural location using genome editing (BIOL-207), and watch the tagged protein move through the living cell.

Fluorescence works because a fluorophore absorbs light of one wavelength and emits light of a longer wavelength a few nanoseconds later. Filters separate the dim emitted light from the much brighter excitation light, so labelled structures appear bright on a dark background. Several colours can be used together. Besides fluorescent proteins, cell biologists use antibodies carrying synthetic dyes (immunofluorescence), small dyes that bind particular structures, such as DAPI for DNA and phalloidin for actin filaments, and self-labelling protein tags such as HaloTag and SNAP-tag, which bind bright synthetic dyes added to the cells. Biosensors are engineered fluorescent proteins whose brightness or colour changes when they bind calcium, cyclic AMP or another signal, or when a kinase phosphorylates them, so that signalling events can be watched in real time.

A tag can change the behaviour of the protein it marks. A fluorescent protein is about 27 kDa, as large as many of the proteins it labels, and it can block a targeting signal at one end or interfere with binding partners. Careful experiments test whether the tagged protein still works, for example by showing that it rescues cells lacking the untagged version.

Beyond the widefield microscope

In a conventional widefield fluorescence microscope, light from out-of-focus planes blurs the image of thick specimens. Several designs reduce this blur.

Breaking the diffraction limit

As BIOL-107 explained, a lens cannot focus light to a point smaller than about half its wavelength. For green light and a good oil-immersion objective, the lateral resolution is roughly 200 to 250 nm, which is larger than many of the structures cell biologists care about: a ribosome is about 25 nm across, a microtubule 25 nm and a synaptic vesicle 40 nm.

Super-resolution methods, recognized by the 2014 Nobel Prize in Chemistry for Eric Betzig, Stefan Hell and William Moerner, get around this limit by controlling which molecules emit light at any moment. In stimulated emission depletion (STED) microscopy, a doughnut-shaped beam switches off fluorescence everywhere except a tiny central spot, so the effective spot can be made much smaller than the diffraction limit. In single-molecule localization microscopy (PALM and STORM), only a sparse random subset of photoswitchable fluorophores is switched on at a time; because each glowing molecule is isolated, its centre can be located far more precisely than the width of its blurred image, and thousands of frames are combined into a final picture. Structured illumination microscopy (SIM) uses striped patterns of light and computation to double the resolution with gentler illumination suitable for living cells. Expansion microscopy takes a different route: the specimen is embedded in a swellable gel and physically enlarged about four-fold or more before imaging with an ordinary microscope.

Electron microscopy in three dimensions

Electron microscopy still provides the highest resolution of cellular structure. Classical preparations, fixed with chemicals, embedded in plastic, sectioned and stained with heavy metals, gave the images that defined the organelles. Freezing cells so fast that water forms a glass rather than ice, a technique developed by Jacques Dubochet, preserves them in a near-native state. In single-particle cryo-electron microscopy, images of thousands of identical purified complexes are averaged to determine their structures at near-atomic resolution; Dubochet, Joachim Frank and Richard Henderson shared the 2017 Nobel Prize in Chemistry for this work. In cryo-electron tomography (cryo-ET), a thin slice of a frozen cell, often milled with a focused ion beam, is imaged at many tilt angles, and the images are combined into a three-dimensional reconstruction showing ribosomes on the ER, the nuclear pore complex in place and the filaments of the cytoskeleton as they exist in the cell.

Correlative light and electron microscopy (CLEM) combines the two worlds: fluorescence identifies the cell, structure or moment of interest, and electron microscopy of the same sample reveals its fine structure.

From images to numbers

A digital image is a grid of numbers, each pixel recording the light collected at one position. Quantifying an image means turning those numbers into measurements that can be compared between cells and experiments. Some basic rules apply. The raw intensity must be corrected by subtracting the background, the light measured where there is no labelled structure. The detector must not be saturated, because saturated pixels hide real differences. Images to be compared must be collected with the same settings. And because a single cell can be unusual, measurements are made on many cells from independent experiments, and summarized with appropriate statistics.

A common question is whether two proteins are in the same place. If one protein is labelled green and another red, colocalization can be assessed by comparing the intensities of the two colours pixel by pixel. Pearson’s correlation coefficient, r, ranges from −1 to +1: values near +1 mean that pixels bright in one channel tend to be bright in the other.

import numpy as np
rng = np.random.default_rng(214)

# Synthetic 128 x 128 images: puncta (vesicles) in two channels
size = 128
yy, xx = np.mgrid[0:size, 0:size]
def puncta(spots, width=2.0):
    img = np.zeros((size, size))
    for (cy, cx) in spots:
        img += np.exp(-((yy - cy)**2 + (xx - cx)**2) / (2 * width**2))
    return img

shared = rng.uniform(5, size - 5, size=(40, 2))
green_only = rng.uniform(5, size - 5, size=(20, 2))
red_only = rng.uniform(5, size - 5, size=(20, 2))

green = puncta(np.vstack([shared, green_only])) + rng.normal(0, 0.05, (size, size))
red_coloc = puncta(np.vstack([shared, red_only])) + rng.normal(0, 0.05, (size, size))
red_random = puncta(rng.uniform(5, size - 5, size=(60, 2))) + rng.normal(0, 0.05, (size, size))

def pearson(a, b):
    a, b = a.ravel(), b.ravel()
    return np.corrcoef(a, b)[0, 1]

print(f"Pearson r, green vs partly colocalized red: {pearson(green, red_coloc):.2f}")
print(f"Pearson r, green vs randomly placed red:    {pearson(green, red_random):.2f}")
print(f"Pearson r, green vs itself:                 {pearson(green, green):.2f}")

Pearson r, green vs partly colocalized red: 0.68
Pearson r, green vs randomly placed red:    -0.03
Pearson r, green vs itself:                 1.00

The partly colocalized pair gives a clearly positive coefficient, the random pair a value near zero. Real analyses also report Manders’ coefficients, which measure what fraction of one signal overlaps the other, and they use controls such as rotating one image to estimate the overlap expected by chance. Colocalization at light-microscope resolution means only that two molecules are within about 200 nm of each other, not that they bind; methods such as Förster resonance energy transfer (FRET), which reports distances under about 10 nm, or proximity labelling are needed to show close association.

Watching molecules move: FRAP

Fluorescence recovery after photobleaching (FRAP) measures how freely labelled molecules move. A strong laser pulse destroys the fluorescence in a small region. Unbleached molecules from the surroundings then move into the region and fluorescence recovers. The speed of recovery reflects how fast the molecules diffuse or exchange, and the extent of recovery shows what fraction is mobile; molecules anchored to a fixed structure do not move in, so recovery is incomplete.

A simple model describes recovery as an exponential approach to a plateau. Fitting this model gives the half-time of recovery and the mobile fraction. For a circular bleached spot of radius w and free two-dimensional diffusion, a widely used approximation estimates the diffusion coefficient as D ≈ 0.224 w² / t½.

import numpy as np
from scipy.optimize import curve_fit
rng = np.random.default_rng(214)

# Simulated FRAP data for a membrane protein (normalized intensities)
F_initial = 1.0          # intensity before bleaching
t = np.linspace(0, 60, 61)            # seconds after the bleach
true = 0.15 + (0.80 - 0.15) * (1 - np.exp(-t / 6.0))
data = true + rng.normal(0, 0.015, t.size)

def model(t, F0, Finf, tau):
    return F0 + (Finf - F0) * (1 - np.exp(-t / tau))

(F0, Finf, tau), _ = curve_fit(model, t, data, p0=[0.1, 0.7, 5])
t_half = tau * np.log(2)
mobile = (Finf - F0) / (F_initial - F0)
w = 1.0                  # radius of bleached spot, um
D = 0.224 * w**2 / t_half
print(f"fitted F0 = {F0:.2f}, plateau = {Finf:.2f}, tau = {tau:.1f} s")
print(f"half-time of recovery = {t_half:.1f} s")
print(f"mobile fraction = {mobile:.2f}  (immobile {1 - mobile:.2f})")
print(f"estimated D = {D:.3f} um^2/s for a 1 um spot")

fitted F0 = 0.16, plateau = 0.80, tau = 6.1 s
half-time of recovery = 4.2 s
mobile fraction = 0.77  (immobile 0.23)
estimated D = 0.053 um^2/s for a 1 um spot

The fitted values say that about three-quarters of the labelled protein can move and that it diffuses with a coefficient of a few hundredths of a square micrometre per second, typical of membrane proteins. By comparison, a small soluble protein such as GFP diffuses in the cytoplasm at roughly 20 to 30 µm²/s, about a thousand times faster. Real FRAP analyses must account for diffusion during the bleach, binding and unbinding, and the shape of the bleached region, but the idea is the same.

Other quantitative approaches

Several other methods complement imaging. Flow cytometry measures the fluorescence of thousands of individual cells per second as they pass a laser in a stream, giving distributions rather than single images; lesson 12 uses it to measure DNA content through the cell cycle. Cell fractionation and proteomics, which identify and quantify thousands of proteins in each fraction by mass spectrometry, map which proteins belong to which organelle; large projects such as the Human Protein Atlas, which images the location of thousands of human proteins with antibodies, have shown that roughly half of human proteins are found in more than one compartment. Proximity labelling attaches an enzyme to a protein of interest that tags nearby proteins with biotin, revealing its neighbourhood. And single-cell sequencing measures gene expression in individual cells, revealing variation hidden in averages.

Good practice with images

Images are data and are subject to the same standards of honesty as any other data. Journals expect that adjustments to brightness and contrast are applied to the whole image and to controls equally, that no features are added, removed or moved, and that the original files are kept. Duplicated or manipulated images are a common reason for retraction of papers. Canadian researchers funded by the federal granting agencies follow the Tri-Agency Framework: Responsible Conduct of Research, while US researchers funded by federal agencies are covered by research misconduct rules that treat fabrication and falsification of images as misconduct.